Geodesic
About the spectrum of the Laplace operator
Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 129-133

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The famous French scientist J. Hadamard constructed the well-known example illustrating the incorrectness of the Cauchy problem for the Laplace equation. Since then, the question arises whether there exists a Volterra problem for the Laplace equation. In this paper we prove a theorem for a wide class of correct restrictions of the maximal operator $\widehat L$ and the correct extensions of the minimal operator $L_0$, generated by the Laplace operator, which are not Volterra problems. 
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     title = {About the spectrum of the {Laplace} operator},
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B. N. Biyarov. About the spectrum of the Laplace operator. Eurasian mathematical journal, Tome 2 (2011) no. 2, pp. 129-133. http://geodesic.mathdoc.fr/item/EMJ_2011_2_2_a6/